Make a taming room with dino gate and door. Eat a few rare flowers and fly over the jungle to agro a few pteras. Fly back to room, dismount and enter the room with pteras following. Shut gate, exit door, wait for buff to drop, safely tame at your leisure.
When knocking pteranodons out, be sure to have a bola, it doesn't take many tranq arrows to knock it out. Once it is down, put spike walls up around it (with a little space so you can go in and out) so it doesn't lose taming efficiency or die.
To kill pretty much anything on these birds, tame a high level, then pump stam to 3k, then the remainder in melee. Barrel roll into alphas etc. But keep eye on Stam. Never regen Stan on ground, know your ledges!